3.321   ODE No. 321

\[ \boxed { \left ( 2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{3}+{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-2\,x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,y \left ( x \right ) -1=0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.181023 (sec), leaf count = 47 \[ \text {Solve}\left [\frac {1}{64} \left (-4 y(x)^2+4 y(x)-2 \log (8 y(x)+4)+3\right )-\frac {1}{4 x (2 y(x)+1)}=c_1,y(x)\right ] \]

Maple: cpu = 0.125 (sec), leaf count = 42 \[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it RootOf} \left ( x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{3}-4\,x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}+8\,{\it \_C1}\,x{{\rm e}^{{\it \_Z}}}+2\,{\it \_Z} \,x{{\rm e}^{{\it \_Z}}}+3\,x{{\rm e}^{{\it \_Z}}}+16 \right ) }}}{2}}- {\frac {1}{2}} \right \} \]